I'd like to identify the set of corner portfolios so that I can interpolate the entire efficient frontier. A corner portfolio defines a segment on the minimum-variance frontier within which i) portfolios hold identical assets, and ii) the rate of change of asset weights in moving from one portfolio to another is constant. Incidentally, The Global Minimum Variance portfolio is a corner portfolio.

Any convex combination of two adjacent corner portfolios is also a portfolio on the efficient frontier. So these corner portfolios can drastically improve the performance of tracing out the frontier.

Are there tools in R to identify the corner portfolios, or a research paper on an efficient algorithm to identify the portfolios? Markowitz himself introduced the critical line algorithm, however, I recall Sharpe and others have some approaches as well. R or matrix calculus approaches are preferred but I'll take research citations as well.

Correct me if I'm wrong, but efficient frontier is a linear combination of any two efficient portfolios.
–
Alexey KalmykovDec 23 '12 at 8:46

1

No - an efficient portfolio is only a linear combination of any two corner portfolios.
–
Quant GuyDec 23 '12 at 20:31

Are you sure? Check the paper provided in the answer by Bryce, page 4, in the bottom: "The the set of eﬃcient portfolios of risky assets can be computed as a convex combination of any two eﬃcient portfolios."
–
Alexey KalmykovDec 23 '12 at 20:34

*Also, see zivot links below. "The the set of efficient portfolios of risky assets can be computed as a convex combination of any two efficient portfolios."
–
patDec 25 '12 at 7:41

I think there are two different questions to be considered here: "How to calculate corner portfolios?" and "How to generate the efficent frontier?" The second question can be answered by the mutual fund separation theorem - at least if the asset weights should sum to one (or total wealth). If you impose weight constraints, I don't know. I think the other comments refer to the mutual fund separation theorem.
–
vanguard2kJan 7 at 12:28

2 Answers
2

7 years ago I had to solve the problem of a efficiency frontier under linear constraints on the asset weights and also stumbled upon Markowitz Critial Line Algorithm. I still have a directory with some resources in it.

Since Bryce already gave a practical implementation with R code by Eric Zivot, I will concentrate on some papers which might help.